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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/* -------------------------------------------------------------------------*</span></div><div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">*                               SPHinXsys                                   *</span></div><div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">* --------------------------------------------------------------------------*</span></div><div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">* SPHinXsys (pronunciation: s&#39;finksis) is an acronym from Smoothed Particle *</span></div><div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">* Hydrodynamics for industrial compleX systems. It provides C++ APIs for    *</span></div><div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">* physical accurate simulation and aims to model coupled industrial dynamic *</span></div><div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">* systems including fluid, solid, multi-body dynamics and beyond with SPH   *</span></div><div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">* (smoothed particle hydrodynamics), a meshless computational method using  *</span></div><div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">* particle discretization.                                                  *</span></div><div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">*                                                                           *</span></div><div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">* SPHinXsys is partially funded by German Research Foundation               *</span></div><div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">* (Deutsche Forschungsgemeinschaft) DFG HU1527/6-1, HU1527/10-1             *</span></div><div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">* and HU1527/12-1.                                                          *</span></div><div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">*                                                                           *</span></div><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">* Portions copyright (c) 2017-2020 Technical University of Munich and       *</span></div><div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">* the authors&#39; affiliations.                                                *</span></div><div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment">*                                                                           *</span></div><div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">* Licensed under the Apache License, Version 2.0 (the &quot;License&quot;); you may   *</span></div><div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">* not use this file except in compliance with the License. You may obtain a *</span></div><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment">* copy of the License at http://www.apache.org/licenses/LICENSE-2.0.        *</span></div><div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment">*                                                                           *</span></div><div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment">* --------------------------------------------------------------------------*/</span></div><div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="preprocessor">#ifndef SPHINXSYS_BASE_SMALLVEC_H</span></div><div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="preprocessor">#define SPHINXSYS_BASE_SMALLVEC_H</span></div><div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;</div><div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="preprocessor">#pragma once</span></div><div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;</div><div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="preprocessor">#include &lt;cmath&gt;</span></div><div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="preprocessor">#include &lt;cassert&gt;</span></div><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;</div><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="preprocessor">#include &quot;Simbody.h&quot;</span></div><div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="preprocessor">#include &quot;SimTKcommon.h&quot;</span></div><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="preprocessor">#include &quot;SimTKmath.h&quot;</span></div><div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="preprocessor">#include &quot;scalar_functions.h&quot;</span></div><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="preprocessor">#include &lt;algorithm&gt;</span></div><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="preprocessor">#include &lt;map&gt;</span></div><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;</div><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="keyword">using namespace </span><a class="code" href="namespacestd.html">std</a>;</div><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespace_s_p_h.html">SPH</a> {</div><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;</div><div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <span class="keyword">template</span>&lt;<span class="keywordtype">int</span> N, <span class="keyword">class</span> T&gt;</div><div class="line"><a name="l00044"></a><span class="lineno"><a class="line" href="class_s_p_h_1_1_s_vec.html">   44</a></span>&#160;    <span class="keyword">class </span><a class="code" href="class_s_p_h_1_1_s_vec.html">SVec</a></div><div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    {</div><div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    <span class="keyword">private</span>:</div><div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;</div><div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;        T v[N];</div><div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;</div><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    <span class="keyword">public</span>:</div><div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;</div><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a>()</div><div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        {</div><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;                v[i] = (T)0;</div><div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;        }</div><div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;</div><div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        <span class="keyword">explicit</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a>(T value_for_all)</div><div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        {</div><div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;                v[i] = value_for_all;</div><div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        }</div><div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;</div><div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">class</span> S&gt;</div><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        <span class="keyword">explicit</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a>(<span class="keyword">const</span> S *source)</div><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        {</div><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;                v[i] = (T)source[i];</div><div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        }</div><div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;</div><div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">class</span> S&gt;</div><div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;        <span class="keyword">explicit</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a>(<span class="keyword">const</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, S&gt;</a>&amp; source)</div><div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;        {</div><div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;                v[i] = (T)source[i];</div><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        }</div><div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;</div><div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">class</span> S&gt;</div><div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        <span class="keyword">explicit</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a>(<span class="keyword">const</span> SimTK::Vec&lt;N, S&gt;&amp; source)</div><div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;        {</div><div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;                v[i] = (T)source[i];</div><div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        }</div><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;</div><div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a>(T v0, T v1)</div><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;        {</div><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;            v[0] = v0; v[1] = v1;</div><div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;        }</div><div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;</div><div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a>(T v0, T v1, T v2)</div><div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        {</div><div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;            v[0] = v0; v[1] = v1; v[2] = v2;</div><div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;        }</div><div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;</div><div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;        T &amp;operator[](<span class="keywordtype">int</span> index)</div><div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;        {</div><div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;            assert(index &gt;= 0 &amp;&amp; index &lt; N);</div><div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;            <span class="keywordflow">return</span> v[index];</div><div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;        }</div><div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;</div><div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;        <span class="keyword">const</span> T &amp;operator[](<span class="keywordtype">int</span> index)<span class="keyword"> const</span></div><div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;            assert(index &gt;= 0 &amp;&amp; index &lt; N);</div><div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;            <span class="keywordflow">return</span> v[index];</div><div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;        }</div><div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;        </div><div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        <span class="keywordtype">bool</span> nonzero(<span class="keywordtype">void</span>)<span class="keyword"> const</span></div><div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                <span class="keywordflow">if</span> (v[i]) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        }</div><div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;</div><div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        <span class="keywordtype">bool</span> operator==(<span class="keyword">const</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a>&amp; b)<span class="keyword"> const</span></div><div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;            <span class="keywordtype">bool</span> res = <span class="keyword">true</span>;</div><div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;                res = res &amp;&amp; (v[i] == b[i]);</div><div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;            <span class="keywordflow">return</span> res;</div><div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;        }</div><div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;</div><div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        <span class="keywordtype">bool</span> operator!=(<span class="keyword">const</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a>&amp; b)<span class="keyword"> const</span></div><div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;            <span class="keywordtype">bool</span> res = <span class="keyword">false</span>;</div><div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;                res = res || (v[i] != b[i]);</div><div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;            <span class="keywordflow">return</span> res;</div><div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;        }</div><div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;</div><div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;        <span class="comment">// Arithmetic operators</span></div><div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator=(<span class="keyword">const</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a>&amp; b)</div><div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        {</div><div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;                v[i] = b.v[i];</div><div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;        }</div><div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;</div><div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator+(<span class="keywordtype">void</span>)<span class="keyword"> const</span></div><div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;            <span class="keywordflow">return</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec</a>(*<span class="keyword">this</span>);</div><div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;        }</div><div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;</div><div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator+=(T a)</div><div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;        {</div><div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;                v[i] += a;</div><div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;        }</div><div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;</div><div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator+(T a)<span class="keyword"> const</span></div><div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;            <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> w(*<span class="keyword">this</span>);</div><div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;            w += a;</div><div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;            <span class="keywordflow">return</span> w;</div><div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        }</div><div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;</div><div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator+=(<span class="keyword">const</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> &amp;w)</div><div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;        {</div><div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;                v[i] += w[i];</div><div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;        }</div><div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;</div><div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator+(<span class="keyword">const</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> &amp;w)<span class="keyword"> const</span></div><div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;            <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> sum(*<span class="keyword">this</span>);</div><div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;            sum += w;</div><div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;            <span class="keywordflow">return</span> sum;</div><div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;        }</div><div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;</div><div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator-=(T a)</div><div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;        {</div><div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;                v[i] -= a;</div><div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;        }</div><div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;</div><div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator-(T a)<span class="keyword"> const</span></div><div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;            <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> w(*<span class="keyword">this</span>);</div><div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;            w -= a;</div><div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;            <span class="keywordflow">return</span> w;</div><div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;        }</div><div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;</div><div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator-=(<span class="keyword">const</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> &amp;w)</div><div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;        {</div><div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;                v[i] -= w[i];</div><div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;        }</div><div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;</div><div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;        <span class="comment">// unary minus</span></div><div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator-(<span class="keywordtype">void</span>)<span class="keyword"> const</span></div><div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;            <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> negative;</div><div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;                negative.v[i] = -v[i];</div><div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;            <span class="keywordflow">return</span> negative;</div><div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;        }</div><div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;</div><div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;        <span class="comment">// minus</span></div><div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator-(<span class="keyword">const</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> &amp;w)<span class="keyword"> const</span></div><div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;            <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> diff(*<span class="keyword">this</span>);</div><div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;            diff -= w;</div><div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;            <span class="keywordflow">return</span> diff;</div><div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;        }</div><div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;</div><div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;        <span class="comment">// scalar product</span></div><div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator*=(T a)</div><div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;        {</div><div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;                v[i] *= a;</div><div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;        }</div><div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;</div><div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator*(T a)<span class="keyword"> const</span></div><div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;            <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> w(*<span class="keyword">this</span>);</div><div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;            w *= a;</div><div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;            <span class="keywordflow">return</span> w;</div><div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;        }</div><div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;        </div><div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator*=(<span class="keyword">const</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> &amp;w)</div><div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;        {</div><div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;                v[i] *= w.v[i];</div><div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;        }</div><div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;</div><div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator*(<span class="keyword">const</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> &amp;w)<span class="keyword"> const</span></div><div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;            <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> componentwise_product;</div><div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;                componentwise_product[i] = v[i] * w.v[i];</div><div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;            <span class="keywordflow">return</span> componentwise_product;</div><div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;        }</div><div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;</div><div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator/=(T a)</div><div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;        {</div><div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;                v[i] /= a;</div><div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;        }</div><div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;</div><div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator/(T a)<span class="keyword"> const</span></div><div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;            <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> w(*<span class="keyword">this</span>);</div><div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;            w /= a;</div><div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;            <span class="keywordflow">return</span> w;</div><div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;        }</div><div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;</div><div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator/=(<span class="keyword">const</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> &amp;w)</div><div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;        {</div><div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;                v[i] /= w.v[i];</div><div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;        }</div><div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;</div><div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;        <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> operator/(<span class="keyword">const</span> <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> &amp;w)<span class="keyword"> const</span></div><div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;            <a class="code" href="class_s_p_h_1_1_s_vec.html">SVec&lt;N, T&gt;</a> componentwise_divide;</div><div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; N; ++i)</div><div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;                componentwise_divide[i] = v[i] / w.v[i];</div><div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;            <span class="keywordflow">return</span> componentwise_divide;</div><div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;        }</div><div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;    };</div><div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;</div><div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;    <span class="keyword">template</span>&lt;<span class="keywordtype">int</span> N, <span class="keyword">class</span> T&gt;</div><div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;    std::ostream &amp;operator&lt;&lt;(std::ostream &amp;out, const SVec&lt;N, T&gt; &amp;v)</div><div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;    {</div><div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;        out &lt;&lt; <span class="charliteral">&#39;[&#39;</span> &lt;&lt; v[0];</div><div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; N; ++i)</div><div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;            out &lt;&lt; <span class="charliteral">&#39; &#39;</span> &lt;&lt; v[i];</div><div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;        out &lt;&lt; <span class="charliteral">&#39;]&#39;</span>;</div><div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;        <span class="keywordflow">return</span> out;</div><div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;    }</div><div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;</div><div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    <span class="keyword">template</span>&lt;<span class="keywordtype">int</span> N, <span class="keyword">class</span> T&gt;</div><div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;    std::istream &amp;operator &gt;&gt; (std::istream &amp;in, SVec&lt;N, T&gt; &amp;v)</div><div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;    {</div><div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;        in &gt;&gt; v[0];</div><div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; N; ++i)</div><div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;            in &gt;&gt; v[i];</div><div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;        <span class="keywordflow">return</span> in;</div><div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;    }</div><div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;</div><div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;    <span class="comment">//vetor with integers</span></div><div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;    <span class="keyword">using</span> Vec2i = SVec&lt;2, int&gt;;</div><div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;    <span class="keyword">using</span> Vec3i = SVec&lt;3, int&gt;;</div><div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;</div><div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    <span class="comment">//vector with unsigned int</span></div><div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    <span class="keyword">using</span> Vec2u = SVec&lt;2, size_t&gt;;</div><div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;    <span class="keyword">using</span> Vec3u = SVec&lt;3, size_t&gt;;</div><div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;</div><div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;    <span class="comment">//float point number</span></div><div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    <span class="keyword">using</span> <a class="code" href="class_real.html">Real</a> = SimTK::Real;</div><div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;</div><div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;    <span class="comment">//useful float point constants </span></div><div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;    <span class="keyword">const</span> SimTK::Real Pi = SimTK::Pi;</div><div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;    <span class="keyword">const</span> SimTK::Real Infinity = SimTK::Infinity;</div><div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;    <span class="keyword">const</span> SimTK::Real Eps = SimTK::Eps;</div><div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;    <span class="keyword">const</span> SimTK::Real TinyReal = SimTK::TinyReal;</div><div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;</div><div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;    <span class="comment">//vector with float point number</span></div><div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;    <span class="keyword">using</span> Vec2d = SimTK::Vec2;</div><div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    <span class="keyword">using</span> Vec3d = SimTK::Vec3;</div><div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;</div><div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;    <span class="comment">//small matrix with float point number</span></div><div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;    <span class="keyword">using</span> Mat2d = SimTK::Mat22;</div><div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    <span class="keyword">using</span> Mat3d = SimTK::Mat33;</div><div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    <span class="comment">//small symmetric matrix with float point number</span></div><div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;    <span class="keyword">using</span> SymMat2d = SimTK::SymMat22;</div><div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;    <span class="keyword">using</span> SymMat3d = SimTK::SymMat33;</div><div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;</div><div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;    Vec2d FirstAxisVector(Vec2d zero_vector);</div><div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;    Vec3d FirstAxisVector(Vec3d zero_vector);</div><div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;    <a class="code" href="class_real.html">Real</a> getMinAbsoluteElement(Vec2d input);</div><div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;    <a class="code" href="class_real.html">Real</a> getMinAbsoluteElement(Vec3d input);</div><div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;    Vec3d upgradeToVector3D(<a class="code" href="class_real.html">Real</a> input);</div><div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;    Vec3d upgradeToVector3D(Vec2d input);</div><div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;    Vec3d upgradeToVector3D(Vec3d input);</div><div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;</div><div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;    Mat2d getInverse(Mat2d &amp;A);</div><div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;    Mat3d getInverse(Mat3d &amp;A);</div><div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;    Mat2d getAverageValue(Mat2d &amp;A, Mat2d &amp;B);</div><div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;    Mat3d getAverageValue(Mat3d &amp;A, Mat3d &amp;B);</div><div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;    Mat2d <a class="code" href="namespace_s_p_h.html#a20e52f12c598f53ec54a7d83ad9faf4c">inverseCholeskyDecomposition</a>(Mat2d &amp;A);</div><div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;    Mat3d <a class="code" href="namespace_s_p_h.html#a20e52f12c598f53ec54a7d83ad9faf4c">inverseCholeskyDecomposition</a>(Mat3d &amp;A);</div><div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;</div><div class="line"><a name="l00335"></a><span class="lineno"><a class="line" href="class_s_p_h_1_1_transform2d.html">  335</a></span>&#160;    <span class="keyword">class </span><a class="code" href="class_s_p_h_1_1_transform2d.html">Transform2d</a> </div><div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;    {</div><div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;        <span class="keyword">using</span> Real = SimTK::Real;</div><div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;        Real rotation_angle_;</div><div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;        Vec2d translation_;</div><div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;    <span class="keyword">public</span>:</div><div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;        <a class="code" href="class_s_p_h_1_1_transform2d.html">Transform2d</a>(SimTK::Real rotation_angle)</div><div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;            : rotation_angle_(rotation_angle), translation_(0) {};</div><div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;        <a class="code" href="class_s_p_h_1_1_transform2d.html">Transform2d</a>(SimTK::Real rotation_angle, Vec2d translation)</div><div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;            : rotation_angle_(rotation_angle), translation_(translation) {};</div><div class="line"><a name="l00346"></a><span class="lineno"><a class="line" href="class_s_p_h_1_1_transform2d.html#a3bcf770fc06aa051e05bb44e6254957d">  346</a></span>&#160;        Vec2d <a class="code" href="class_s_p_h_1_1_transform2d.html#a3bcf770fc06aa051e05bb44e6254957d">ImposeTransform</a>(Vec2d&amp; origin) {</div><div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;            Vec2d result(origin[0] * cos(rotation_angle_) - origin[1] * sin(rotation_angle_),</div><div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;                origin[1] * cos(rotation_angle_) + origin[0] * sin(rotation_angle_));</div><div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;                <span class="keywordflow">return</span> result + translation_;</div><div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;        };</div><div class="line"><a name="l00352"></a><span class="lineno"><a class="line" href="class_s_p_h_1_1_transform2d.html#a0c56696e54acfd4921260fe11f189d64">  352</a></span>&#160;        Vec2d <a class="code" href="class_s_p_h_1_1_transform2d.html#a0c56696e54acfd4921260fe11f189d64">ImposeInverseTransform</a>(Vec2d&amp; result) {</div><div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;            Vec2d origin(result[0] * cos(-rotation_angle_) - result[1] * sin(-rotation_angle_),</div><div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;                result[1] * cos(-rotation_angle_) + result[0] * sin(-rotation_angle_));</div><div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;            <span class="keywordflow">return</span> origin - translation_;</div><div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;        };</div><div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;    };</div><div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;    Vec2d <a class="code" href="namespace_s_p_h.html#a4213991138524c24ecf8c7428055e47e">getCrossProduct</a>(Vec2d &amp;A, Vec2d &amp;B);</div><div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;    Vec3d <a class="code" href="namespace_s_p_h.html#a4213991138524c24ecf8c7428055e47e">getCrossProduct</a>(Vec3d &amp;A, Vec3d &amp;B);</div><div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;    Mat2d <a class="code" href="namespace_s_p_h.html#a3ccbe24cc4474ca5c304de9a061ecfee">getCrossProductMatrix</a>(Vec2d &amp;A);</div><div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    Mat3d <a class="code" href="namespace_s_p_h.html#a3ccbe24cc4474ca5c304de9a061ecfee">getCrossProductMatrix</a>(Vec3d &amp;A);</div><div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;</div><div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div><div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;    std::vector&lt;T&gt; subvector(std::vector&lt;T&gt; <span class="keyword">const</span> &amp;v, <span class="keywordtype">int</span> m, <span class="keywordtype">int</span> n) </div><div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;    {</div><div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;        <span class="keyword">auto</span> first = v.begin() + m;</div><div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;        <span class="keyword">auto</span> last = v.begin() + n + 1;</div><div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;        std::vector&lt;T&gt; sub_vector(first, last);</div><div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;        <span class="keywordflow">return</span> sub_vector;</div><div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;    }</div><div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;</div><div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div><div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;    <span class="keywordtype">void</span> shuffle(std::vector&lt;T&gt; &amp;v) </div><div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;    {</div><div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;        <span class="keywordtype">int</span> size = v.size();</div><div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; size - 1; i++) </div><div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;        {</div><div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;            <span class="keywordtype">int</span> j = i + rand() % (size - i);</div><div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;            swap(v[i], v[j]);</div><div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;        }</div><div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;    }</div><div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;</div><div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div><div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    <span class="keywordtype">void</span> ascendingSort(std::vector&lt;T&gt; &amp;v) </div><div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;    {</div><div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;        <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;i: v)</div><div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;            sort(v.begin(), v.end());</div><div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;    }</div><div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;</div><div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div><div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    <span class="keywordtype">void</span> descendingSort(std::vector&lt;T&gt; &amp;v) </div><div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;    {</div><div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;        <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> &amp;i: v)</div><div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;            sort(v.begin(), v.end(), std::greater&lt;T&gt;() );</div><div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;    }</div><div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;</div><div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div><div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;    std::vector&lt;T&gt; differenceVector(std::vector&lt;T&gt; &amp;a, std::vector&lt;T&gt; &amp;b) </div><div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;    {</div><div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;        std::vector&lt;T&gt; difference_v;</div><div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;        ascendingSort(a);</div><div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;        ascendingSort(b);</div><div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;        set_difference(a.begin(), a.end(), b.begin(), b.end(), </div><div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;                        std::inserter(difference_v, difference_v.begin()));</div><div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;        <span class="keywordflow">return</span> difference_v;</div><div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;    }</div><div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;</div><div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">typename</span> T, <span class="keyword">typename</span> U&gt;</div><div class="line"><a name="l00411"></a><span class="lineno"><a class="line" href="class_s_p_h_1_1create__map.html">  411</a></span>&#160;    <span class="keyword">class </span><a class="code" href="class_s_p_h_1_1create__map.html">create_map</a></div><div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;    {</div><div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;    <span class="keyword">private</span>:</div><div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;        std::map&lt;T, U&gt; m_map;</div><div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;    <span class="keyword">public</span>:</div><div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;        <a class="code" href="class_s_p_h_1_1create__map.html">create_map</a>(<span class="keyword">const</span> T&amp; key, <span class="keyword">const</span> U&amp; val)</div><div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;        {</div><div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;            m_map[key] = val;</div><div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;        }</div><div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;</div><div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;        <a class="code" href="class_s_p_h_1_1create__map.html">create_map&lt;T, U&gt;</a>&amp; operator()(<span class="keyword">const</span> T&amp; key, <span class="keyword">const</span> U&amp; val)</div><div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;        {</div><div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;            m_map[key] = val;</div><div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div><div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;        }</div><div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;</div><div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;        <span class="keyword">operator</span> std::map&lt;T, U&gt;()</div><div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;        {</div><div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;            <span class="keywordflow">return</span> m_map;</div><div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;        }</div><div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;    };</div><div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;}</div><div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;</div><div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;<span class="preprocessor">#endif //SPHINXSYS_BASE_SMALLVEC_H</span></div><div class="ttc" id="class_s_p_h_1_1_s_vec_html"><div class="ttname"><a href="class_s_p_h_1_1_s_vec.html">SPH::SVec</a></div><div class="ttdef"><b>Definition:</b> small_vectors.h:44</div></div>
<div class="ttc" id="class_s_p_h_1_1create__map_html"><div class="ttname"><a href="class_s_p_h_1_1create__map.html">SPH::create_map</a></div><div class="ttdef"><b>Definition:</b> small_vectors.h:411</div></div>
<div class="ttc" id="class_s_p_h_1_1_transform2d_html_a0c56696e54acfd4921260fe11f189d64"><div class="ttname"><a href="class_s_p_h_1_1_transform2d.html#a0c56696e54acfd4921260fe11f189d64">SPH::Transform2d::ImposeInverseTransform</a></div><div class="ttdeci">Vec2d ImposeInverseTransform(Vec2d &amp;result)</div><div class="ttdef"><b>Definition:</b> small_vectors.h:352</div></div>
<div class="ttc" id="namespace_s_p_h_html_a4213991138524c24ecf8c7428055e47e"><div class="ttname"><a href="namespace_s_p_h.html#a4213991138524c24ecf8c7428055e47e">SPH::getCrossProduct</a></div><div class="ttdeci">Vec2d getCrossProduct(Vec2d &amp;A, Vec2d &amp;B)</div><div class="ttdef"><b>Definition:</b> small_vectors.cpp:163</div></div>
<div class="ttc" id="namespace_s_p_h_html_a3ccbe24cc4474ca5c304de9a061ecfee"><div class="ttname"><a href="namespace_s_p_h.html#a3ccbe24cc4474ca5c304de9a061ecfee">SPH::getCrossProductMatrix</a></div><div class="ttdeci">Mat2d getCrossProductMatrix(Vec2d &amp;A)</div><div class="ttdef"><b>Definition:</b> small_vectors.cpp:176</div></div>
<div class="ttc" id="namespacestd_html"><div class="ttname"><a href="namespacestd.html">std</a></div></div>
<div class="ttc" id="class_real_html"><div class="ttname"><a href="class_real.html">Real</a></div></div>
<div class="ttc" id="class_s_p_h_1_1_transform2d_html"><div class="ttname"><a href="class_s_p_h_1_1_transform2d.html">SPH::Transform2d</a></div><div class="ttdoc">Coordinate transfrom in 2D. </div><div class="ttdef"><b>Definition:</b> small_vectors.h:335</div></div>
<div class="ttc" id="namespace_s_p_h_html_a20e52f12c598f53ec54a7d83ad9faf4c"><div class="ttname"><a href="namespace_s_p_h.html#a20e52f12c598f53ec54a7d83ad9faf4c">SPH::inverseCholeskyDecomposition</a></div><div class="ttdeci">Mat2d inverseCholeskyDecomposition(Mat2d &amp;A)</div><div class="ttdef"><b>Definition:</b> small_vectors.cpp:107</div></div>
<div class="ttc" id="class_s_p_h_1_1_transform2d_html_a3bcf770fc06aa051e05bb44e6254957d"><div class="ttname"><a href="class_s_p_h_1_1_transform2d.html#a3bcf770fc06aa051e05bb44e6254957d">SPH::Transform2d::ImposeTransform</a></div><div class="ttdeci">Vec2d ImposeTransform(Vec2d &amp;origin)</div><div class="ttdef"><b>Definition:</b> small_vectors.h:346</div></div>
<div class="ttc" id="namespace_s_p_h_html"><div class="ttname"><a href="namespace_s_p_h.html">SPH</a></div><div class="ttdef"><b>Definition:</b> base_body_supplementary.cpp:11</div></div>
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